Cylinder Volume and Radius Relationships

The video tutorial explains how to calculate the radius of a cylinder given its height and volume. It starts with an intuitive approach, suggesting that if a cylinder's height increases, its radius must decrease to maintain the same volume. The formula for the radius is derived from the volume formula of a cylinder. The tutorial then applies this formula to a problem where a second cylinder is 100 times taller but has the same volume, resulting in a radius that is 1/10th of the original. The solution is verified through mathematical reasoning.

What is the formula used by Jill to calculate the radius of a cylinder?

• r = v * h / pi

• r = pi * v * h

• r = sqrt(v / (pi * h))

• r = v / (pi * h)

If a cylinder's height is increased while keeping the volume constant, what happens to its radius?

• The radius remains the same

• The radius becomes zero

• The radius decreases

• The radius increases

What is the volume formula for a cylinder?

• Volume = pi * r^2 * h

• Volume = 2 * pi * r * h

• Volume = pi * r * h

• Volume = r^2 * h

How does the radius change if the height of a cylinder is increased by a factor of 100?

• The radius remains unchanged

• The radius decreases by a factor of 100

• The radius decreases by a factor of 10

• The radius increases by a factor of 100

What is the square root of 1/100?

• 100

• 1/10

• 1/100

• 10

What is the radius of the second cylinder if the first cylinder's radius is 20 meters and the height is increased by 100 times?

• 1 meter

• 2 meters

• 10 meters

• 20 meters

Why does the radius decrease by a factor of 10 when the height increases by a factor of 100?

• Because the volume decreases

• Because the radius is squared in the volume formula

• Because the height is squared in the volume formula

• Because the volume increases

What is the principal square root of 100?

• 20

• 50

• 10

• 5

What is the relationship between the height and radius of a cylinder when the volume is constant?

• Height and radius are inversely proportional

• Height and radius are unrelated

• Height and radius are directly proportional

• Height and radius are equal

What is the final radius of the second cylinder?

• 20 meters

• 10 meters

• 5 meters

• 2 meters